To find the missing factor [tex]\( B \)[/tex] that satisfies the equation
[tex]\[ -35x^6 = (-5x^2)B, \][/tex]
we can follow these steps:
1. Start with the given equation:
[tex]\[ -35x^6 = (-5x^2)B. \][/tex]
2. Isolate [tex]\( B \)[/tex]:
To isolate [tex]\( B \)[/tex], we need to divide both sides of the equation by [tex]\(-5x^2\)[/tex]. This gives us:
[tex]\[ \frac{-35x^6}{-5x^2} = B. \][/tex]
3. Simplify the fraction:
Simplify the left-hand side of the equation:
[tex]\[ \frac{-35x^6}{-5x^2} = \frac{35x^6}{5x^2}. \][/tex]
4. Divide the coefficients:
Divide [tex]\( 35 \)[/tex] by [tex]\( 5 \)[/tex]:
[tex]\[ \frac{35}{5} = 7. \][/tex]
5. Divide the variables:
For the variable part, apply the rule of exponents [tex]\( \frac{x^a}{x^b} = x^{a-b} \)[/tex]:
[tex]\[ \frac{x^6}{x^2} = x^{6-2} = x^4. \][/tex]
6. Combine the results:
Multiply the results from the coefficient and variable parts:
[tex]\[ 7 \cdot x^4 = 7x^4. \][/tex]
Therefore, the value of [tex]\( B \)[/tex] that satisfies the equation [tex]\(-35x^6 = (-5x^2)B\)[/tex] is:
[tex]\[ B = 7x^4. \][/tex]
If we need only the coefficient of [tex]\( B \)[/tex], it is:
[tex]\[ B = 7. \][/tex]
So, the missing factor [tex]\( B \)[/tex] that makes the equality true is
[tex]\[ \boxed{7}. \][/tex]
